The SSS Co has a patent on a particular medication. The medication sells for $1 per daily dose and marginal cost is estimated to be a constant at 20¢

Assuming linear demand and marginal cost curves, use this information to estimate the deadweight loss from monopoly pricing if the firm currently sells 1,000 doses per day. Can this loss be justified?

The firm's Lerner Index equals 0.8 which implies an elasticity of -1.25. To solve for the slope of the demand curve, set -1.25 = (dQ/dp) ? (p/Q) or dQ/dp = -1250. The demand curve is
Q = a - 1250p. Since we know that Q = 1000 when p = $1, a = 2250. Thus the demand curve is
Q = 2250 - 1250p. This implies that Q would be 2000 if the market were competitive and price were 20¢. The deadweight loss per day is [(1 - 0.20 ) ? (2000 - 1000 )]/2 = $400. This loss can be justified on the grounds that had the patent not been issued, the medication might not exist at all.